I think you've read too much into some of the comments. No one is suggesting winning the French cup is a massive achievement. PSG should obviously win everything in France every single year. He became manager in January was PSG manager for less than 6 months of the season and won a cup. In his first full season he's 11 points clear. That's not arguments as to why he's a sensational winner, it's just facts.
His most impressive achievements are by far how he built Southampton into a very entertaining side, and had Spurs punching well above their weight with significant budget constraints. That's why most Pochettino supporters believe he'd do well - not his two half-seasons at PSG.
I agree fully that there are questions about his ability to win trophies - I personally believe he can with the right club, but there's plenty of arguments as to why not. Obviously that is a fair discussion and a fair point to make. My issue is with the characterisation of his mentality as a "quitter" just because he'd want to join us instead of winning the French league and another cup with PSG.